The voters in question live mainly in Eastham, a small, fractured district of the Wirral overlooking the Mersey, and one so far largely ignored in the frantic coverage of the constituency.
Known at the turn of the century as the Richmond of the Mersey for its attractive waterside landscape, Eastham has become the Lib Dems' sole strong- hold in Wirral South, and was largely responsible for the 6,581 votes the party managed at the last general election. But this support could collapse come polling day because the Lib-Dems are seen as running a lacklustre campaign with a third-choice candidate from Liverpool.
Eastham's electorate is now being eyed greedily by Labour, acutely aware that to overturn an 8,000-plus Conservative majority they need all the anti-Tory support they can muster.
Ironically for a party which fears the Ashdown threat in a number of key seats, the Tories, too, are worried - by what they see as a sluggish start to the Lib-Dem campaign. "They seem to have put up the white flag. We have seen very little of them," says Tory candidate, Les Byrom. The real Tory fear is that if the Lib-Dems voters desert the party it will be to Labour's likeable candidate, Ben Chapman.
The Lib-Dems have not started well. When their preferred candidate, Phil Gilchrist, declined to enter the race, they chose Neil Thomas, chief executive of a training organisation. But he withdrew after a legal row with his employers.
Finally, Flo Clucas, a prominent councillor across the Mersey, stepped in. She is indignant at the "white flag" jibe, and at a Tory suggestion that she is fighting a single-issue campaign on war pensions. "If anything, it's the Conservatives who have only one issue - with grammar schools," she says, referring to endless attempts to put Labour on the spot over the future of two local selective schools. "Health, the police and standards in education are the issues that people care about."
Mrs Clucas is quick to reject the old claim that in a by-election so close to a national poll, a Lib-Dem vote is a wasted one. "If you want to change the Government and compel the Labour Party to spend more money on education, then the way to vote is for the Liberal Democrats."
So far she says she is encouraged by the doorstep response. But Labourites and Tories feel she could suffer from the "Liverpool factor" and lose supporters through her association with this city; a link underlined on Friday when Liverpool MP David Alton turned up to back her campaign. Certainly Mrs Clucas, an education tutor at Liverpool Hope University, is far better known there, where she is deputy leader of the party's council group.
Labour activists have moved in fast, setting up a campaign outpost in the heart of Liberal Democrat territory. They know that despite media expectations of a spectacular win, Wirral South has a solid Tory vote of almost 25,000 at each election, more than half the overall vote. Mr Chapman believes the message is getting across. On the Mill Park estate - full of "aspirant classes" - it seems the Lib-Dems may be losing to Labour. But analysis of the Eastham ward, which has at least three distinct areas, is difficult.